Usually yes — plain Mucinex (guaifenesin) is an expectorant in a different drug class from ibuprofen and the two are not listed as interacting, but FIRST read the label, because many Mucinex combo products already contain a pain reliever or NSAID, and you must not double up.
The main active ingredient in plain Mucinex is guaifenesin, an expectorant that thins and loosens chest mucus, while ibuprofen is a nonsteroidal anti-inflammatory drug (NSAID) that relieves pain, fever, and inflammation — different mechanisms, and neither drug's MedlinePlus page lists the other as an interaction. The catch is that "Mucinex" is a brand with many multi-symptom versions (e.g., Sinus-Max, Fast-Max), and some of these combination products contain an NSAID or another pain reliever. The NHS warns plainly: do not take ibuprofen at the same time as other NSAIDs such as naproxen or aspirin, and check the leaflet that comes with your medicine to see what to avoid. Taking ibuprofen on top of a product that already contains an NSAID means doubling up, which raises the risk of stomach ulcers and bleeding. So the answer hinges entirely on which Mucinex you have: plain guaifenesin is generally fine alongside ibuprofen, but a combination product may not be.
Read the Drug Facts label on your Mucinex box before adding ibuprofen. If the only active ingredient is guaifenesin, taking it with ibuprofen is not expected to interact — just dose each correctly: per MedlinePlus, nonprescription ibuprofen for adults is generally no more than 6 doses in 24 hours, used at the lowest effective dose for the shortest time. If the label also lists ibuprofen, aspirin, naproxen, or any other NSAID, do NOT add a separate ibuprofen — that is doubling the NSAID, and the NHS warns this raises the risk of stomach ulcers and bleeding; if it lists acetaminophen/paracetamol or a decongestant (e.g., phenylephrine/pseudoephedrine) or dextromethorphan ("DM"), that's a separate reason to check with a pharmacist so you don't overlap ingredients. Be especially careful with ibuprofen if you have a history of stomach ulcers or GI bleeding, kidney or liver disease, heart disease, high blood pressure, asthma, or are pregnant (MedlinePlus says do not take ibuprofen around or after 20 weeks of pregnancy unless your doctor tells you to), or take a blood thinner such as warfarin. Stop and seek care for stomach pain, black or bloody stools, vomiting blood, chest pain, or shortness of breath. Call a doctor if a cough lasts more than 7 days or fever/pain persists beyond about 3 days, and check with a pharmacist whenever you're unsure or take other prescription medicines.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.